From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4153 Path: news.gmane.org!not-for-mail From: "Ronnie" Newsgroups: gmane.science.mathematics.categories Subject: Re: Cartesian closed without products Date: Tue, 8 Jan 2008 21:29:50 -0000 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain;format=flowed; charset="iso-8859-1";reply-type=original Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019756 11948 80.91.229.2 (29 Apr 2009 15:42:36 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:42:36 +0000 (UTC) To: Original-X-From: rrosebru@mta.ca Wed Jan 9 19:34:05 2008 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 09 Jan 2008 19:34:05 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1JCkEB-0001IS-Hi for categories-list@mta.ca; Wed, 09 Jan 2008 19:20:55 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 14 Original-Lines: 24 Xref: news.gmane.org gmane.science.mathematics.categories:4153 Archived-At: Toby Bartels wrote: > > OTOH, the version without unit probably has some use, > just as non-monoid semigroups occasionally do. Just a thought that this interest may be more than occasional: inverse semigroups are closely related to pseudogroups and so are part of Charles Ehresmann local-to-global view and interests, with a deep relation to ordered groupoids (see further work by Mark Lawson). So all these partial units express something on the *local* structure, even if there is a global unit. My paper with Aof (based on ideas of Pradines) uses an inverse semigroup generated by continuous local admissible sections. (with M. E.-S. A.-F. AOF), ``The holonomy groupoid of a locally topological groupoid'', {\em Top. and its Appl.}, 47 (1992) 97-113. Is this a rash view that one should look more at inverse categories? Ronnie Brown